Batteries are a useful source of stored energy that can be incorporated into a number of systems. Rechargeable lithium-ion (Li-ion) batteries are attractive energy storage systems for portable electronics and electric and hybrid-electric vehicles because of their high specific energy compared to other electrochemical energy storage devices. In particular, batteries with a form of lithium metal incorporated into the negative electrode afford exceptionally high specific energy (in Wh/kg) and energy density (in Wh/L) compared to batteries with conventional carbonaceous negative electrodes. Li-ion batteries also exhibit lack of hysteresis and low self-discharge currents. Accordingly, lithium-ion batteries are a promising option for incorporation into electric vehicles (EV), hybrid electric vehicles (HEV) and plug-in hybrid electric vehicles (PHEV).
One requirement for incorporation of batteries including Li-ion batteries into EV/HEV/PHEV systems is the ability to accurately compute the state of charge (SOC) and state of health (SOH) of the batteries in real time. SOC is a percentage which reflects the available energy in a cell compared to the available energy of the cell when fully charged. SOC is thus akin to the fuel gauge provided on fossil fuel based vehicles.
SOH is a general term which encompasses a variety of quantities and is in the form of a percentage which reflects the presently available energy and power in a cell assuming the cell to be fully charged compared to the available energy and power of the cell when fully charged at beginning of cell life. SOH is thus akin to the size of the fuel tank provided on fossil fuel based vehicles and the health of the engine to provide the power. Unlike the volume of a fuel tank and the power output of an engine, the SOH of a cell decreases over cell life as discussed more fully below.
Both SOC and SOH are needed to understand, for example, the available range of a vehicle using the cell and the available power. In order to provide SOH/SOC data, a battery management system (BMS) is incorporated into a vehicle to monitor battery parameters and predict SOH/SOC.
Various algorithms have been proposed for use in a BMS to maintain the battery system within safe operating parameters as well as to predict the actual available power in the battery system. One such approach based on an electrochemical paradigm is described by N. Chaturvedi, R. Klein, J. Christensen, J. Ahmed, and A. Kojic, “Algorithms for advanced battery-management systems,” IEEE Control Systems Magazine, 30(3), pp. 49-68, 2010. Generally, in order to accurately estimate the SOH of a system, the SOC of the system must be accurately known. Conversely, in order to accurately estimate the SOC of a system, the SOH of the system must be accurately known.
SOC estimation, even when an accurate SOH is available, is challenging since simple methods of predicting SOC, such as Coulomb Integration, suffer from increased errors over increased integration time. The increased errors result from biased current measurements or discretization errors as reported by S. Piller, M Perrin, and A. Jossen, “Methods for state-of-charge determination and their applications,” Journal of Power Sources, 96, pp. 113-120, 2001. Nonetheless, some approaches such as the approach described by U.S. Pat. No. 7,684,942 of Yun et al. use pure current integration to determine SOC and then derive SOH from the determined SOC.
Other approaches avoid exclusive reliance upon current integration by combining current integration with a form of SOC estimation to obtain an SOC as a weighted sum of both methods as disclosed in U.S. Pat. No. 7,352,156 of Ashizawa et al. In another approach reported by K. Ng, C. Moo, Y. Chen, and Y. Hsieh, “Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries,” Journal of Applied Energy, 86, pp. 1506-1511, 2009, the result obtained from current integration is reset in accordance with an OCV/SOC look-up table.
All of the foregoing approaches, however, rely upon obtaining a dependable initial value for the cell SOC. If a dependable initial value for cell SOC is not available, the described methods fail. Unreliable SOC values are commonly encountered during drive cycles or when switching off current. For example, during driving cycles or when switching off current, the dynamics of the battery may not decay to zero or settle at a steady-state level at the precise moment that a measurement is obtained. Thus a calculation depending upon an observed voltage may be biased if the voltage is obtained during a transient.
Other approaches such as those described in U.S. Patent Publication No. 2010/0076705 of Liu et al., U.S. Pat. No. 7,615,967 of Cho et al., and U.S. Patent Publication No. 2005/0231166 of Melichar work only in discrete special cases and are not guaranteed to work robustly during normal operation of a battery. These approaches may further incur increased errors as a battery ages with use.
Many advanced BMSs incorporate various forms of a Kalman filter such as those reported by H. Dai, Z. Sun, and X. Wei, “Online SOC Estimation of High-power Lithium-ion Batteries used on HEV's,” Vehicular Electronics and Safety, ICVES, 2006, and J. Lee, O. Nam, and B. Cho, “Li-ion battery SOC estimation method based on the reduced order extended Kalman Filtering,” Journal of Power Sources, 174, pp. 9-15, 2007. BMSs incorporating Kalman filters, however, are based upon an assumption of known and time-invariant parameters incorporated into a battery model. In a real battery system the various parameters vary on both a long-term and short-term basis. For example, battery aging alters the capacity and internal resistance of the battery over the long term. Thus, the SOH of the battery changes over cell lifetime introducing errors into SOC calculations. Moreover, temperature and rate of current draw vary over the short term and both temperature and rate of current draw affect the SOC determination. Accordingly, while accurate knowledge of the present SOH of the battery is a prerequisite for accurate SOC determination in approaches incorporating Kalman filters, such information may not be readily available.
Accurate estimation of SOH is likewise challenging. A good estimator has to be able to track battery model parameters on a short time scale to account for the parameters' dependence or rate of current draw, SOC, and temperature, and also on a long time scale to account for changing health of the battery. Estimators which operate when the battery is placed off-line have been proposed. Placing a battery offline in order to determine remaining driving range, however, is typically not possible. Moreover, this approach is not recursive resulting in increased computational expense. Thus, such off-line approaches are of limited value in providing near real-time estimation which is needed during operation of a vehicle.
Additionally, approaches which require stable input parameters, which may be available when a system is offline, cannot provide accurate estimates when presented with disturbances in the measured battery parameter signals like voltage and current noise, gain errors and/or measurement bias. Moreover, since the open circuit voltage (OCV) of most batteries is nonlinear, a direct application of standard parameter estimation theory which is directed to estimating a constant value is not possible. Accordingly, accurate knowledge of the present SOC of the battery is a prerequisite for accurate SOH determination. U.S. Pat. No. 7,352,156 of Ashizawa et al. addresses this issue by assuming a linearized model with an initially known OCV. As the actual SOC diverges from the assumed linear model, however, estimation errors are incurred and can eventually result in divergence of the estimator. Thus, known systems rely on the actual SOC or incorporate excess robustness into the SOH estimation to allow for SOC errors.
Accordingly, accurately estimating SOH and SOC presents a circular problem in known systems with accurate estimation of one parameter depending upon accurate foreknowledge of the other of the two parameters. Some attempts have been made to solve the circular problem by performing a combined estimation of both parameters. Such approaches have been reported by G. Plett, “Extended Kalman Filtering for battery management systems of LiPB-based HEV battery packs Part3. State and parameter estimation,” Journal of Power Sources, 134, pp. 277-292, 2004, and M. Roscher and D. Sauer, “Dynamic electric behavior and open-circuit-voltage modeling of LiFePO4-based lithium ion secondary batteries,” Journal of Power Sources, 196, pp. 331-336, 2011. These approaches, however, are computationally expensive.
An alternative approach to solving the circular SOH/SOC problem is to incorporate extended or unscented Kalman filters as reported by G. Plett, “Sigma-point Kalman Filtering for battery management systems of LiPB-based HEV battery packs. Part 2: Simultaneous state and parameter estimation,” Journal of Power sources, 161, pp. 1369-1384, 2006. This approach, however, is also computationally expensive.
What is needed therefore is a battery system incorporating a BMS which can estimate the nominal capacity of a battery without prior knowledge of either battery SOC or SOH. A system which is much more robust than known approaches given initial inaccuracies such as unknown current sensor noise or bias would be beneficial. A system which accurately estimates nominal capacity of a battery without excessive computational cost would be further advantageous.